CHAPTER 1
ISSUES IN TENSE SEMANTICS
This dissertation investigates the semantics of tense and the temporal interpretation of tensed and tenseless predicates in natural language. Tense is a well-studied topic in the semantics literature.1 There are a number of theories of tense, many of which are successful in accounting for the intuitive meanings of tensed sentences like Elliott is in Japan and Jen went to Boston. Examination of the tense interpretation of these simplex, unembedded sentences does not discriminate one tense theory from another, nor does it tell us much about what ingredients are necessary for the proper treatment of tense in natural language.
For this reason (and perhaps more), many authors have investigated tense interpretations of more complex sentences that have one or more tenses embedded under another.
Earlier researchers, such as Saarinen (1979) and Cresswell (1990), conclude that the natural language tense system must be such that it is able to keep track of all times
introduced in a given sentence.2 This helps narrow down the number of theories of tense.
Many existing theories can in this regard be shown to be empirically inadequate. Among the theories that meet this criterion, we will consider two here: a tense system that employs overt quantification over times in the object language, and a system with infinitely many evaluation indices and operators that control them. (We will further articulate this distinction in § 1.1.) These two systems have been proven to be equivalent in terms of expressive power. (See Cresswell 1990.) In this dissertation, we present some evidence that favors the former system, one with explicit quantification over times in the object language.
Recent researchers, such as Ogihara (1989, 1995b, 1996), Stowell (1993, 1995a,b), Abusch (1994, 1997a), von Stechow (1995a,b), Heim (1994), and Kratzer (1998b),
1 See Kuhn (1989) for a brief summary of many issues on tense and related topics.
See also Binnick (1991).
2 For an overview of this issue, see van Benthem (1977).
investigate tense in embedded contexts from a different perspective. These authors focus on particular phenomena called the sequence of tense (SOT) phenomena. The phenomena are typically found in clausal complements of so-called propositional attitude verbs like believe and say. Informally speaking, in languages like English, the present tense in a direct quotation such as Eva said, "Elliott is in Japan." becomes the past tense in its indirect quotation counterpart such as Eva said that Elliott was in Japan.3 These authors have contributed a great deal to our understanding of tense in embedded contexts as well as tense in general. Yet there still remain some underinvestigated issues and unsolved puzzles. For example, whether a similar analysis can be carried over to other embedded contexts such as relative clauses and adjunct clauses remains unsolved.
A closely related but much less studied topic is the temporal interpretation of expressions that are not tensed (at least not in English). In the area of the temporal interpretation of noun phrases, there are two major contributions: Enç (1981, 1986) and Musan (1995). The temporal interpretation of other non-tensed expressions such as noun modifiers (adjectives, participles, etc.) has not received much attention, though.
Another issue that has not received enough attention concerns languages that do not exhibit the SOT phenomena, such as Japanese, Polish, and Russian. Unlike languages like English, these languages use the same tense form in both direct and indirect quotations. We will call these languages non-SOT languages. The fact that the SOT phenomena are not universal is well known. Cross-linguistic studies comparing SOT and non-SOT languages show this (Comrie 1985, Ogihara 1989, 1996). Less well-known is the fact that there is a striking difference among non-SOT languages in their tense interpretation in embedded contexts other than clausal complements.
In this dissertation, we bring these issues together and seek a theory of tense that has more empirical coverage both within and across languages. In particular, we propose that
3 This is a very informal description of the phenomena. The phenomena are not limited to cases of quotations. Also the change is not obligatory for many native speakers.
That is, sentences like Eva said that Elliott is in Japan are grammatical. We will discuss the SOT phenomena in details in § 1.5.1.
tense morphemes are time variables that saturate the time argument slots of predicates they 'modify'. This proposal implies that event times of predicates are represented in the object language only when the predicates are tensed.4 It predicts differences between tensed and tenseless expressions in their temporal interpretations. We will examine new data from English and Japanese that support this distinction. We will then look more closely at differences among non-SOT languages. We will see that the proposed tense system with limited overt quantification over times in the object language gives a straightforward account of the observed difference among non-SOT languages.
1.1. Preliminary: Formalities and Assumptions
Let us now return to issues of quantification over time in the object language vs. in the meta- language only. Suppose that Elliott went to Japan on August 20th and came back to the States on December 27th, and that this is the only trip to Japan he made. The sentence Elliott is in Japan would be true when uttered at 3:00 PM on September 15th but it would not when uttered at 3:00 PM on July 4th or December 31st. The sentence Elliott was in Japan would be true when it is uttered at 3:00 PM on December 31st, but not on July 4th.5 As this example illustrates, the truth conditions of a sentence usually vary depending on when the sentence is evaluated. In most cases, it is when the sentence is uttered, i.e., the speech time.6
4 We will use the term 'event' to cover both events and states.
5 When uttered on September 15th, while Elliott is still in Japan, the sentence Elliott was in Japan is true but misleading. It can give rise to an implicature that he is no longer in Japan. Whether such an implicature arises or not depends on the context in which the sentence is uttered. Issues of context dependency are discussed below.
6 This is not always the case, as Barbara Partee (p.c.) pointed out to me. (This is first discussed in Kratzer 1978, according to Partee.) Take the case of a message on my answering machine: "I am unable to come to the phone now." In normal circumstances, the sentence is not evaluated with respect to the time I say it, i.e., the time of my recording, but with respect to a time somebody calls me when I am not home. I can think of two ways to accommodate cases like this. One is to say that sentences are evaluated with respect to a time that is made salient in the context. In many cases, it is the speech time, but in cases like the above, it is the time of calling. The other way is to say that sentences are always
This means that sentence denotations have to be relativized with respect to times.
We can do this by explicitly quantifying over times in the object language or by limiting quantification to the meta-language only. (By the object language, we mean the LF syntactic structure, assuming there is no intermediate level of interpretation.) We will review some of the literature on this issue below, but we refer the reader to Massey (1969), Kamp (1971), Vlach (1973), Partee (1973), Parsons' (1973) and Stalnaker's (1973) replies to Partee, van Benthem (1977), Saarinen (1978), and especially Cresswell (1990).
Since sentence meanings are computed from the meanings of their parts, relativizing sentence denotations with respect to times amounts to relativizing denotations of nouns, verbs, etc with respect to times. In order to determine the truth conditions of a sentence like Elliott was in Japan, we will have to determine the denotations of its parts, such as the
denotations of the noun Elliott and the predicate be-in-Japan.7
Before moving on, let us address one question. What is time? It had often been assumed, for instance in Montague (1974), that time is the set of moments of time. Bennett and Partee (1972) present arguments against this conception of time, and propose that at least some sentences have to be evaluated with respect to intervals of time. One of the strongest arguments for interval-based semantics comes from accomplishment predicates.
Suppose, for instance, that I baked a cake from 3:00 PM to 5:00 PM today. It would not be true to say that I baked a cake at the initial moment of my cake baking time, 3:00 PM. If it were, I would be able to say, "I baked a cake" at 4:00 PM when I was still in the middle of the cake baking. It would also not be true that I baked a cake at the final moment of my cake baking time, 5:00 PM, nor would it be true that I baked a cake at all moments of time between 3:00 and 5:00. We must say that I baked a cake at the interval from 3:00 PM to 5:00 PM. Thus we would want the domain of times to include not only moments of time
evaluated with respect to the speech time. But a caller takes my recorded message "as if" I am speaking at the moment.
7 We treat complex predicates like be-in-Japan as single lexical entries.
but also intervals of time. See Dowty (1979) and Cresswell (1985) for more arguments and discussion.8
Let us resume our discussion on tense now. Consider first a system with overt quantification over times in the object language, in which we have the following in terms of type theory. We include worlds here since we will eventually need to introduce possible world semantics when we discuss tense in clausal complements. But we will ignore world variables (or indices) for the moment.
(1) a. e, t, i, and s are types
b. For any types and , <,> is a type c. Nothing else is a type
We define semantic domains as follows. The model we assume consists of D, the set of all individuals, T, the set of all intervals, and W, the set of all worlds.
(2) a. De = D
b. Dt = the set of truth values, i.e., {0,1}
c. Di = T
d. Ds = W
e. For any types and , D<,> is the set of functions from D to D
The interpretation function is defined relative to a variable assignment function and a context index: for any expression , [[]]g,c is the denotation of with respect to a variable
assignment function g and a context index c. A variable assignment is a partial function that
8 See Tichy (1985) for arguments against an interval-based semantics.
assigns each variable of type a member of D. For any variable x of type with an index i, [[xi,]]g,c = g(i,).9
The denotations of Elliott and be-in-Japan in this framework are the following, ignoring world variables:
(3) a. [[Elliott]]g,c = Elliott
b. [[be-in-Japan]]g,c = f: De D<i,t>
For any t Di and x De, f(x)(t)= 1 iff x is in Japan at t
Proper names like Elliott denote individuals. Predicates like be-in-Japan, which are 'ordinarily' considered as one-place predicates are actually two-place predicates in this framework; they take an individual argument and a time argument.10 Here we assume that the individual argument is the first argument and the time argument is the outermost one.
The mere assumption that predicates take an extra argument for a time does not necessarily mean that we choose to represent times overtly in the object language. By overt quantification over times in the object language, we mean to have LF structures like the following, where the time argument of the predicate be-in-Japan is saturated by a time variable ti. (In what follows, many of the LF structures are annotated with their interpretations. These interpretations are, however, not part of the LF representations.)
9 We will omit a specification of types when there is no confusion and write [[xi]]g,c = g(i) instead.
10 By 'ordinarily', we mean before the introduction of event arguments by Davidson (1967). Since then, many arguments for an event-argument analysis have been presented in the literature. (See Parsons 1990 and Landman 1990, among others.) What we claim in this thesis is that predicates contain an argument slot that has temporal information. We identify it as a time argument for convenience. We are not claiming that event arguments should be replaced by time arguments. In fact, it has been argued in Parsons (1990) that events cannot be individuated just by their times, and we agree with him. Whether it is necessary to posit both event arguments and time arguments or whether event arguments can do all the work is an interesting and perhaps an important issue, but it is beyond the scope of this thesis.
(4) a. [be-in-Japan(ti)(Elliott)]
4
ti t[be-in-Japan(t)(Elliott)]
4
Elliott xt[be-in-Japan(t)(x)]
$
be-in-Japan
b. [[(4a)]]g,c = 1 iff Elliott is in Japan at g(i)
The truth conditions of the whole structure are computed using the following interpretation rules. (See Heim and Kratzer 1998.)
(5) a. Terminal Node
If is a terminal node, [[]] is specified in the lexicon.
b. Functional Application
If is a branching node, {, } is the set of 's daughters, and [[]] is a function whose domain contains [[]], then [[]] = [[]]([[]]).
What introduces the time variable ti? Is it a phonologically null pronominal element, or does it have a morphological realization? This is a question that remains to be answered.
Consider next a system where times are manipulated only in the meta-language, in which we have only two basic semantic types, e, and t. Instead of having the semantic type i, the interpretation function is relativized with respect to an interval in addition to an
assignment function and a context index. (Recall that we are ignoring world indices.) For any expression , [[]]g,c,t is the denotation of with respect to a variable assignment function g, a context index c, and an interval t.
(6) a. [[be-in-Japan]]g,c,t = f: De Dt
For any x De, f(x)= 1 iff x is in Japan at t b.
4
Elliott $ be-in-Japan
c. [[(6b)]]g,c,t = 1 iff Elliott is in Japan at t
The choice between the two systems seems a technical matter at this point. But it does affect the semantics of tense, and when we look at complex sentences with two or more tenses, it ultimately results in empirical differences, as we will see below.
1.2. A Starting Point: Priorian Tense Logic
We have seen that the truth conditions of most sentences vary among other things depending on when the sentences are uttered, i.e., the speech time. And tenses affect the truth conditions. We take this to be uncontroversial and ask the following questions: What system does natural language employ to express the speech time dependency? How do tenses come into the system?
One answer is given in Prior (1967), further developed in Montague (1974):
sentence denotations are relative to a temporal index and tenses are sentential operators that affect the index. For instance, the semantics of the past, present, and future tenses are defined as follows in Priorian tense logic, where t is a temporal index and < is an ordering relation:
(7) Where is a tenseless sentence,
a. [[Past ]]t = 1 iff there is a time t' such that t' < t and [[]]t' = 1
b. [[Pres ]]t = 1 iff [[]]t = 1
c. [[Fut ]]t = 1 iff there is a time t' such that t < t' and [[]]t' = 1 d. [[]]t = 1 iff is true at t
These denotations of tenses imply that (at least) the denotations of predicates are relative to a temporal index:
(8) a. [[Elliott]] = Elliott
b. [[be-in-Japan]]t(x) = 1 iff x is in Japan at t
Given the denotation in (8), we get the desired results.
(9) a. [[Pres Elliott be-in-Japan]]3:00 PM,9/15 = 1 iff Elliott is in Japan at 3:00 PM on September 15.
b. [[Past Elliott be-in-Japan]]3:00 PM,12/31 = 1 iff there is a time t such that t < 3:00 PM December 31st and that Elliott is in Japan at t
(9) correctly predicts that the sentences Elliott is in Japan and Elliott was in Japan are true when evaluated at 3:00 PM, September 15th and at 3:00 PM, December 31st respectively.
The following assumptions are made in this kind of tense semantics: (i) tense
manipulates times only in the meta-language, (ii) tense is a sentential operator, (iii) sentences are evaluated with respect to one temporal index, and (v) tense is an existential quantifier over times.11 There are a few more properties of this tense system that are consequences of these assumptions: tense introduces a new time, this new time becomes the evaluation time, and the original evaluation time is lost. There is also a hidden assumption that the tense operators Past, Pres, and Fut correspond to the past tense morpheme, the present tense morpheme, and the future auxiliary respectively. None of these should be taken for granted
11 The fourth point is only claimed for Past and Future, not for Present.
as necessary assumptions and each has been challenged in the literature explicitly or implicitly.
In this chapter, we will examine these assumptions and their effects, and try to find out what are necessary ingredients for the proper treatment of tense. We take Priorian tense logic as a starting point, and discuss shortcomings of the theory that have been pointed out in the literature. We will then try to fix the analysis without changing the core analysis of Priorian tense logic, as well as present some alternative approaches. These assumptions are not independent of each other and a particular choice for one issue may affect a choice for another issue. Therefore, instead of listing and reviewing all existing theories, we will discuss advantages and disadvantages of theories of tense with respect to the following three issues: issues of explicit quantification over times in natural language, whether tenses are existential quantifiers or not, and issues concerning the relation between what we see (i.e., tense morphemes) and what we understand (i.e., temporal interpretation).
Section 1.3. is devoted to issues of explicit quantification over times in natural language. These issues were discussed extensively in the 1970s in connection with a multiple index tense system proposed in Kamp (1973) and Vlach (1974). Recent
semanticists working on tense simply assume one way or the other, and not much attention has been given to this issue. For instance, Ogihara (1989, 1996) and Abusch (1998) assume quantification only in the meta-language, and Ogihara (1995a) and Abusch (1994, 1997a) assume quantification in the object language. We will examine what have been presented as problems for Priorian tense logic and see what changes have to be made to accommodate the problematic data.
In section 1.4., we will look at the context dependency of tense interpretations. This issue was once considered to be an argument against an existential analysis of tenses. We will see that, as argued in Bäurele (1979), Partee (1984), and Ogihara (1989, 1996),
resorting to a referential analysis of tenses is not a necessary move to account for context dependency.
Issues of explicit quantification over times are also closely related to the question of whether there is a one-to-one correspondence between tense morphemes and the meaning of anteriority and simultaneity. Once we allow explicit quantification over times in the object language, we have at least three elements that are needed for the right understanding of the temporal interpretation: evaluation times, event times of predicates, and the source of the ordering between the two.12 Generally, it is assumed that tenses are what determine the ordering relation between evaluation times and event times. We will discuss the so-called sequence of tense phenomena and the temporal interpretation of non-verbal predicates in section 1.5., which suggests that tense morphemes do not always correspond to what we think they mean and that tense morphemes are not necessary to get temporal interpretations.
Lastly, in section 1.6., we will look at data from languages other than English, such as Japanese, Polish, and Russian. These languages are crucially different from English in that they do not exhibit sequence of tense phenomena. We refer to these languages that do not exhibit the SOT phenomena as non-SOT languages. We will see that not all non-SOT languages behave alike in all embedded contexts. To my knowledge, differences among the non-SOT languages in their temporal interpretations are not discussed in the literature, with the exception of Arregui and Kusumoto (1998), Kusumoto (1998), and Kondrashova (1999). The data presented in this work seem problematic for previous theories of the SOT phenomena that divide languages into SOT and non-SOT languages. In Chapters 2 and 3, we will argue that tense semantics is uniform across non-SOT languages and apparent differences are due to structural differences of the relevant constructions, e.g., relative clauses and temporal adjunct clauses.
12 Many authors, such as Reichenbach (1947) and Klein (1994), claim that there is a third time that is involved in temporal interpretation, i.e., Reichenbach's 'reference time' or Klein's 'topic' time. They claim that tenses relate evaluation times and reference times (or topic times.) One advantage in introducing this third notion is to account for the context dependency of tense interpretation. As we will see later, however, context dependency can also be explained by means of implicit domain restrictions, and the latter system has a wider empirical coverage. Therefore, we will adopt the latter system, although it is possible that we will use both systems for context dependency.
1.3. Does Natural Language Employ Explicit Quantification over Times?
To simplify the discussion, let us assume for the moment that tense is a sentential operator, and that tense involves existential quantification over times. In Priorian tense logic,
sentences are evaluated with respect to one temporal index. As a consequence, whenever tense introduces a new time, the original evaluation time is lost. This makes a particular prediction for cases where one tense is in the scope of another. And this is where it is criticized. Consider the following examples from Kamp (1971):
(10) a. A child was born who would become ruler of the world b. A child was born who will become ruler of the world
The two sentences differ in their tense in the relative clauses. Priorian tense logic posits a future tense operator as defined above. This operator corresponds to both will and would in English. Morphologically, however, the future auxiliary will is present tensed and would is past tensed. This fact is not incorporated into the system. We believe this is because the authors were more concerned with how to represent the intuitive meaning of a sentence using these tense operators than they were with the syntax-semantics mapping. As we will see below, however, will and would are semantically different, and it is natural to assume that the difference between them comes from their difference in tense. We will later decompose the words will and would into the future auxiliary woll, and a present tense and a past tense respectively.13 The future tense operator defined above can be seen as the denotation of the auxiliary woll.14
13 The word woll is used in Abusch (1988).
14 Hall (1964) observes a contrast between (i) and (ii) regarding whether will and would can occur in if-clauses, and claims that there are two different interpretations of will and would, a volitional interpretation and a future interpretation.
(i) a. If everyone will be brief, we can finish almost on time b. If everyone would be brief, we can finish almost on time (ii) a. * If he will see the great white whale, he will try to kill it
b. * If he would see the great white whale, he would try to kill it
Now let us return to the meanings of the sentences in (10a). The first sentence has the representation in (11a) and is predicted to have the truth conditions in (11b) by the tense semantics given in (7).
(11) a. Past [a child be born [Fut who become ruler of the world]]
b. [[(11a)]]t = 1 iff there is a time t' such that t' < t and that there is a child x at t' and x is born at t' and there is a time t" such that t' < t" and that x becomes ruler of the world at t"
The time of a child becoming ruler of the world is placed in the future with respect to the time of his/her birth, and the truth conditions of the sentence do not tell whether or not s/he has already become ruler of the world by the speech time. The second sentence, on the other hand, has different truth conditions: it cannot truthfully be uttered when the speaker knows that the child has already become ruler of the world. The time of his/her becoming ruler has to be located after the speech time.
In order to capture this interpretation, the future operator has to be evaluated with respect to the original evaluation time. However, in Priorian tense logic, after the past tense is introduced in the sentence, it affects the temporal index. It introduces a new time, t', in the meta-language, and the original evaluation time, t, is lost at this point. As a result, the future auxiliary will cannot have access to the original evaluation time, t, when embedded under another tense operator as is the case in (10b). The only temporal index available is t'.
Therefore, Priorian tense logic cannot capture the intuitive meaning of the sentence.
Cf. If he sees the great white whale, he will try to kill it
In this thesis, we will only be concerned with the future interpretation of will and would.
The use of the future will under a past tense operator is not the only case in which Priorian tense logic makes a wrong prediction. A past tense embedded under another past tense provides another case. Consider the following examples:15
(12) a. Hillary married a man who became the president of the U.S.
b. Who hired the person who wrote this article?
If the surface structure is what we interpret, Priorian tense logic predicts that these sentences are true only when the time at which the event described by the matrix predicate takes place - -- the matrix event time --- follows the embedded one. This is because the embedded past tense is in the scope of the matrix past tense. According to the tense semantics, the
embedded past tense takes the new time introduced by the matrix past tense as its evaluation time and places the embedded event time further in the past. However, the sentence (12a) is understood as a true report about Hillary Clinton in 1999, who married Bill Clinton, who became the president after their marriage. Similarly, when uttered by a chief editor, the sentence (12b) is most likely to be understood as a question to find out who is responsible for hiring the person who, after being hired, wrote the article. This type of interpretation where the embedded event time follows the matrix event time has sometimes been called the 'forward-shifted' interpretation. This name seems to imply that the embedded tense is evaluated with respect to the matrix event time and somehow shifted forward. We believe that this is not how we understand the temporal ordering of these sentences. So we will use a more neutral term and call this type of interpretation the later-than-matrix interpretation.16 Priorian tense logic is unable to predict the availability of this interpretation.
Kamp (1973) proposes a two-dimensional system to cope with this situation;
sentences are evaluated with respect to a pair of temporal indices. The first index is like the
15 The (b) example is due to Barbara Partee.
16 The term is suggested by Barbara Partee (p.c.).
one we had before. It is a working index with respect to which sentences are evaluated, and it is affected by tense operators. The second index is to keep the original evaluation time.
He also proposes a new operator N (for now), which takes the stored original evaluation time and sets it as the new evaluation time.
(13) a. [[Past ]]t,t'= 1 iff there is a time t" such that t" < t and [[]]t",t' = 1 b. [[Fut ]]t,t'= 1 iff there is a time t" such that t < t" and [[]]t",t' = 1 c. [[N ]]t,t' = 1 iff [[]]t',t' = 1
d. [[]]t,t' = 1 iff is true at t
With this we can have a representation of the sentence (10b) as follows.
(14) a. Past [a child is born [N [Fut who become ruler of the world]]]
b. [[(14a)]]t,t' = 1 iff there is a time t" such that t" < t and that there is a child x at t" and x is born at t" and there is a time t"' such that t < t"' and that x becomes ruler of the world at t"'
The second index is stored and is not affected by the past tense operator. The N operator takes the stored original evaluation time and sets it as the working evaluation time. And then the future operator is evaluated with respect to the original evaluation time.
Similarly, the speech time dependency of the English simple past in the case of (12) is derived by applying the N operator before the embedded past tense operator as follows:
(15) a. Past [Hillary married a man who N [Past [became the president of the U.S.]]]
b. Past [Who hired the person who N [Past [wrote this article?]]]
The effect of this is that two past tenses are both evaluated with respect to the original evaluation time. The truth conditions of the sentence (15a) for instance, say that both marriage time and the man's becoming the president time are before the original evaluation time. This leaves the two times unordered with respect to each other, predicting the
possibility of the embedded event time following the matrix one.
The two sets of data we examined show that the original evaluation time should always be retrievable. A double-index system like Kamp's allows us to keep track of the original evaluation time and use it whenever we like by using the N operator.
Vlach (1973) presents another argument against a single-index tense system like Priorian tense logic. The following examples show that it is not enough to keep track of the original evaluation time; we need to keep track of the intermediate evaluation times.
(16) a. John was once going to cite everyone who was then speeding
b. The writer complained to a person who hired an editor who he was working with.
For instance, in (16a), the time of speeding is understood to be at the past time when John was going to cite people. This reading is not derived in Priorian tense logic. If we assume that the phrase be going to corresponds to the future operator in Priorian tense logic, the sentence has the logical form of Past Fut John cite ... The future operator introduces a new time, which is a future time with respect to the past time introduced by the past operator. And at this point the time introduced by the past operator is lost.
Vlach proposes an operator which stores an evaluation time introduced by tense operators such as the following:
(17) [[K ]]t,t' = 1 iff [[]]t,t = 1
The sentences in (16) are translated into the following representation:
(18) a. Past K Fut x [ N speeding(x) cite(y)(John)]]]
b. Past K x [person(y) & complain-to(y)(the-writer) & Past y [editor(y) &
hire(y)(x) & N work-with(y)(the-writer)])]
The interpretation of the sentence (16a), for instance, is derived in the following way: the K operator is applied after the matrix past tense operator in order to store a new evaluation time, and the N operator is then used when evaluating the relative clause to retrieve that stored evaluation time. (Here we are only interested in representing possible interpretations for the sentences and ignore the fact that the predicate speeding, for instance, in the object language is past tensed but there is no corresponding past tense operator in the semantic representation below.)
Note that in the representation in (18a), we only store the past time when John was going to cite people and it is this time that the N operator has access to. This means that in this representation, the original evaluation time is not accessible, which it should be,
considering the following sentences.
(19) a. John was going to cite all those who were then speeding, who are now in jail b. The writer complained to a person who hired an editor who he was and still
is working with
To capture the meanings of the examples above, we need to store two times; the original evaluation time and the first intermediate evaluation time that is introduced by the first past tense operator. This means that the two dimensional system is not powerful enough. We need a three-dimensional system. It is not difficult to construct examples where we need four, five or six-dimensional systems, and we can go on indefinitely. This point has been established by authors like Gabbay 1974, Saarinen 1978, and Cresswell 1990. In order to capture what we can express in the English language (or any other natural language), our
tense system must be a multiple-index system where sentences are evaluated with an infinite number of indices, and the K and N operators must be able to be used as many times as we want for each index.
The system should look like the following:17
(20) a. [[Nn ]] = 1 iff [[]][n/0] = 1 b. [[Kn ]] = 1 iff [[]][0/n] = 1
c. [[Past ]] = 1 iff there is a time t such that t < (0) and [[]][t/0] = 1 d. [[Fut ]] = 1 iff there is a time t such that (0) < t and [[]][t/0] = 1 e. [[]] = 1 iff is true at (0)
is any infinite sequence of times. [n/0] is the sequence just like except that [n/0](0) = (n), and [0/n] is the sequence just like except that [0/n](n) = (0).
We continue to simply call this system a multiple-index system, but we exclude systems where we impose a limit on numbers of indices possible. In other words, we will not consider two-, three-, or seventeen-dimensional systems as candidates for a multiple- index system.
A different way of temporally relativizing sentence denotations is to have explicit quantification over temporal variables. Here is one way of implementing this idea. Let us assume that predicates have an extra argument position for a time variable. (Recall that this assumption alone does not guarantee overt quantification over times. We will come back to this issue later.) The denotation of be-in-Japan is now as follows:18
17 From Kratzer (1995b), based on a parallel treatment of world indices in Cresswell (1990).
18 This is not a necessary change to represent event times in the object language.
We could introduce a special predicate such as Dowty's (1979) AT, which introduces time variables in the object language while keeping the denotation of one-place predicates such as be-in-Japan as one-place predicates.
(21) [[be-in-Japan]]g,c = f: De D<i,t>
For any t Di and x De, f(x)(t)= 1 iff x is in Japan at t
The denotations of tense operators are changed minimally from the ones in Priorian tense logic:
(22) a. [[Past]]g,c = f: D<i,t> D<i,t>
For any p D<i,t> and t Di, f(p)(t) = 1 iff there is a time t' such that t' < t and p(t') = 1
b. [[Pres]]g,c = f: D<i,t> D<i,t>
For any p D<i,t> and t Di, f(p)(t) = 1 iff there is a time t' such that t' = t and p(t') = 1
c. [[Fut]]g,c = f: D<i,t> D<i,t>
For any p D<i,t> and t Di, f(p)(t) = 1 iff there is a time t' such that t < t' and p(t') = 1
For simplex sentences like Elliott was in Japan, we have the following structure:
(23) a. Elliott was in Japan
b. t'[t' < t & be-in-Japan(t')(Elliott)]
3
t tt'[t' < t & be-in-Japan(t')(Elliott)]
3
Past t'[be-in-Japan(t')(Elliott)]
3
t' [be-in-Japan(t')(Elliott]
3
t' t[be-in-Japan(t)(Elliott)]
3
Elliott xt[be-in-Japan(t)(x)]
$ be-in-Japan
We will call a time variable that saturates the open slot of a tensed sentence (t in this case) the evaluation time variable of the tense operator, and a time variable that saturates the time argument of the main predicate (t' in this case) the event time variable.19
Note that the semantics given in (21) and (22) does not force syntactic saturation of the temporal argument. This has to be stipulated in this framework.20 We also assume that
19 In simple tensed sentences like Elliott was in Japan and Jen went to Boston, what we call the event time variable saturates the time argument slot of the main predicates such as be-in-Japan and go-to-Boston. In more complex sentences with various auxiliaries, we will have to ask at what point in a structure a time variable appears. For instance, in sentences with Perfect such as John had opened the door, we can assume that a time variable occurs at the VP level and saturates the time argument slot of the predicate open- the-door, or at a higher level above have-en, and saturates the open slot of the clause have- opened-the-door (assuming that have-en is an operator that takes properties of times and returns properties of times), or both. We will not discuss sentences with Perfect, i.e., have- en.
20 One way to force syntactic saturation compositionally is to make the time argument of a predicate the innermost one:
(i) [[be-in-Japan]]g,c = f: Di D<e,t>
For any t Di and x De, f(t)(x)= 1 iff x is in Japan at t
a lambda binder is freely inserted in the LF structure whenever necessary for compositional reasons. For instance, without the abstractor over the variable t', the above structure would be uninterpretable.
Assuming that unbound variables denote the speech time, the truth conditions of the sentence when uttered at 3:00 PM, December 31 are as follows:
(24) [[(23b)]]g,c = 1 iff there is t' < 3:00 PM, December 31st such that Elliott is in Japan at t'
This is the desired result.
How does the system deal with the problematic examples presented against Priorian tense logic? Kamp's sentence receives the following LF. (This LF does not give the word order of the sentence. Since we are concerned with the restrictive interpretation of the relative clause, we assume that this is the structure we interpret. Our analysis of tense interpretation does not rely any of these assumptions.)
(25) a. A child was born who will become ruler of the world b.
4
t 4
Past 4
t' 4
t' 5
3 #
a 3 be born child 3
who 3
t" 3
Fut 3
t"' 3 t"' # become r-of-w
Assuming that the individual argument is syntactically saturated by an NP, this denotation forces syntactic saturation of the temporal argument.
Suppose that unbound variables are understood to denote the speech time. In this representation, the evaluation time variables of the past and future operators, t and t", are unbound, and therefore denote the speech time. As a result, both operators are relative to the speech time irrespective of the scope.
The system also predicts the availability of the later-than-matrix readings of tense in relative clauses correctly. There, the two past tenses have their own evaluation times
explicitly at LF, and they are given values independent of each other.
(26) a. Hillary married a man who became the president
b. 2
t 2
Past 2 t' 2 t' 2
Hillary 2
marry 2 a 2 man 2
who 2
t" 2 Past 2
t"' 2
t"' # become the president
Again assuming that unbound variables denote the speech time, the analysis predicts that the two event times are unordered.
In this system, all times introduced in sentences are represented in the object language. This means that we keep track of not only the original evaluation time, but also the intermediate ones. Therefore we can account for Vlach's examples, too.
(27) a. John was going to cite everyone who was then speeding
b. 2
t 2
Past 2 t' 2 t' 2
Fut 2 t" 2 John 2
cite 2 every 2 one 2
who 2 t' # then speeding
The most embedded event time, the time of speeding, represented as a time variable, is bound by the relevant lambda operator in the higher clauses.
So far, we have considered two tense systems: a multiple-index system and a system with explicit quantification over time in the object language, i.e., the LF structure. (Recall that we are only considering as a multiple-index system a system with infinite number of temporal indices and infinite sets of K and N operators.)
The need for systems like those above has been challenged by Stowell (1993) and Uribe-Exebarria (1993).21 They argue that the relevant readings are derived by means of movement. We will call this a movement analysis. For instance, they argue that a clause containing will cannot be and is not in the scope of the past tense at LF. In the case of Kamp's example, repeated here as (28a), a conceivable LF would be (28b).
(28) a. A child was born who will become ruler of the world b. A child [who Fut become ruler of the world] Past be born
The future auxiliary will in (28b) is no longer in the scope of the past tense and therefore has access to the original evaluation time. Ogihara (1996) dismisses this possibility since it assumes that the subject NP a child is not in the scope of the past tense, predicting that the individual in question has to be a child at the original evaluation time, which it does not have to be.22 The problem of the temporal interpretation of NPs in this particular case can be overcome, however. Enç (1981, 1986) and Musan (1995) argue that the temporal interpretation of an NP is not necessarily dependent on the scope of the tenses of the sentence in which it occurs. According to them, roughly speaking, the fact that the NP a child is not in the scope of the past tense operator does not necessarily mean that the individual under discussion has to be a child at the evaluation time. Enç and Musan each propose a system of temporal interpretation of NPs that does not rely on the scope of tenses. We will come back to this issue in § 1.5.2. If Enç and Musan are right, we can overcome the problem noted by Ogihara in this case.
A similar claim is made for the case of the speech time dependency of embedded past tenses. Authors including Ladusaw (1977), Ogihara (1989, 1996), and Stowell (1993) argue that the later-than-matrix interpretation of past tensed relative clauses is due to
21 They did not present a movement analysis as a challenge to a multiple-index system, though.
22 Ogihara (1996, p.66, footnote 14).
movement like QR (or quantifying-in, depending on the framework they adopt).23 The LF representations we want to interpret should look like the following:
(29) a. [a man who Past become the president]i Hillary Past marry ti b. [the person who Past write this article]i Who Past hire ti ?
In these representations, neither the matrix past tense nor the embedded one is in the scope of the other. Therefore, both tenses are evaluated with respect to the original evaluation time. As a result, the truth conditions of the sentences only require that the time of the man's becoming the president and the marriage time precede the original evaluation time, and no order is given between the two. The later-than-matrix interpretation is compatible with the sentence meaning.
According to proponents of a movement analysis, therefore, the temporal
interpretations of the examples we have considered are not true counterexamples to a single- index system such as Priorian tense logic. They claim that the relevant readings may be derived by movement. However, they have to face the consequences of such movement.
For instance, they have to deal with examples involving other scope-bearing elements. In Chapter 2, we will show that a movement analysis in a single-index system is untenable by examining examples that produce a scope paradox.
23 Partee (1973) already suggested a correlation between tense interpretations and quantifier scope. The following is the example she has:
(i) If John had married Susan, he would have had everything he wanted The sentence is ambiguous; the NP everything he wanted may have a transparent
interpretation in which it 'refers' to everything he wanted in some past time, a time at which he might have married Susan, in the actual world, or an opaque interpretation in which the NP is in the scope of the modal operator. Partee (1973) suggests that the past tense on the verb wanted is deictic on the former interpretation. This leads to an idea that embedded tenses may have an independent interpretation without quantifying in, the idea we will pursue in this thesis.
Barbara Partee (p.c.) has also pointed out to me that the idea of relating tense interpretations and quantifying in was already around possibly in the late 1960s, but I have not been able to locate a published work that discusses the issue explicitly.
Before concluding, we consider another possible way to account for the speech time dependency. That is to adopt an absolute tense theory in the lexical semantics of tenses, which assumes that tenses are always evaluated with respect to the speech time. Ogihara (1996) argues that the speech time dependency of sentences containing will under a past operator is due to a lexical property of will itself. He claims that the future auxiliary will is inherently speech time sensitive. Here is one way to implement his idea.24
(30) [[will]]g,c = f: D<i,t> Dt
For any p D<i,t>, f(p) = 1 iff there is a time t' such that tc < t' and p(t') = 1
Sentences are evaluated with respect to a temporal index and a speech context. Each speech context uniquely determines the speech time tc, and the future will shifts the temporal index to the future from the speech time. The semantics of will above does the job that both future and N operators in Kamp's system do. Thus, it assures a more transparent mapping from syntax to semantic representation.
Whether Ogihara's proposal for the case of will is adequate or not, this solution is not extendable to all the cases of speech time dependency. Consider the following denotation of the past tense:
(31) [[Past]]g,c = f: D<i,t> Dt
For any p D<i,t>, f(p) = 1 iff there is a time t' such that t' < tc and p(t') = 1
This is a direct extension of what is proposed for the future will. This semantics predicts that a past tense, no matter how deeply embedded, always means past with respect to the
24Ogihara analyzes the future auxiliary will as the present tense plus a modal, which he calls woll, the term used in Abusch (1988). The inherent speech time dependency of will stems from the semantics of the present tense, and it does not have to be stipulated in the way we did. Also the proposal presented here as an implementation of Ogihara's claim differs from his actual proposal, which hinges on movement of the future auxiliary will above the past tense.
speech time. Thus, the intended readings of sentences like (12), the Hillary example, may be correctly derived. Since the proposal makes use of two indices after all, we can say that this particular proposal is a variant of Kamp's two-dimensional system. We presented this system as a separate option since we treat it as an example of an absolute tense system. The same results can be achieved by any version of absolute tense theories, including a
referential analysis of tenses, which will be presented in the following section. And the same criticisms are applied, too.
How can this proposal handle Vlach's examples?
(32) a. John was once going to cite everyone who was then speeding b. The writer said that Nancy hired an editor who he was working with
If we analyze the most embedded past tense in the examples as the speech time sensitive past, the semantic representation we get is compatible with the situation where the speeding time and the working time coincide with the matrix past event times.
A problem with this analysis is that it always predicts a speech time dependency for the English simple past. Consider the following examples, however.25
(33) a. I will marry a man who went to Harvard
b. I thought that the student would not admit that he cheated c. David will say that he was out of town
d. No matter what you give him to eat, he will eat it and tell you that he liked it
When uttered by a five year old girl, the sentence (33a) can be true when the man she marries has a degree from Harvard by the time she marries. The sentence (33b) can be
25 Barbara Partee (p.c.) points out that not everyone accepts the past tense usage in (33a). For some speakers, a present perfect has gone has to be used to express a past- relative-to-future-reading.
truthfully uttered when the student in question, who looked suspicious to me, had not yet cheated, and the sentence (33c) can be used to make a guess about what David will say when I ask him the day after tomorrow where he was tomorrow. Similarly for (33d). The semantics of the past tense operator in (31) does not predict past-relative-to-a-future-time interpretations. It is for this reason that Ogihara (1989, 1996), where the indexical analysis of will is proposed, argues that the same analysis should not be carried over to the cases of past tense interpretation.
To conclude, we have seen four theories of tense: Priorian tense logic as an example of a single-index system, a multiple-index system, a system with explicit quantification over times in the object language, and an absolute theory of tense. Contrary to what has been claimed by many authors, the particular examples we considered do not justify the need for a multiple-index system. With LF movement of the appropriate elements, Priorian tense logic does seem to make the correct predictions for those cases. The proponents of this position are left with the tasks of showing that the LF movement necessary to derive the right temporal interpretation is a licit, and hopefully independently motivated one, and dealing with the consequences of such movement in other domains of semantic
interpretation, such as quantifier scope and variable binding. It will be shown in Chapter 2 that this option is inadequate.
A multiple-index system and a system with explicit quantification over times in the object language are alternatives. At the cost of introducing multiple indices or overt
temporal variables, we can deal with the speech time dependency of embedded tenses. This is the cost we have to pay if a single-index system is not an option, and it will be shown that it is not. Making a choice between a system where the speech time dependency is a matter of the meta-language and a system where we quantify explicitly over times is difficult.
Cresswell (1990) shows in Entities and Indices that the expressive power of explicit quantification amounts to having an infinite number of temporal indices and operators that tell us which predicates are associated with which indices. That is, in order to express what
we can express with our language, it must employ either full explicit quantification over times or an infinite number of temporal indices plus an infinite set of the K and N operators.
In a system with overt quantification over times, relations between time variables are represented in LF syntax by means of binding, parallel to pronominal binding. Kamp (1971) and Cresswell (1990) both argue for a system without explicit quantification since according to them, systems with explicit quantification complicate the syntax with extra argument places. This is certainly true. However, in a system without explicit quantification over times, we need a mechanism to derive appropriate syntactic structures with the N and K operators in the right places. We believe that this is at least as considerable a departure from the actual form of the original sentences as a system with extra argument positions in the syntax. Assuming that we believe in explicit quantification over individuals and use mechanisms such as indexing and the Binding Theory to derive relations between two or more variables, we believe that a system with explicit quantification is less stipulative and less complicated. In the chapters that follow, we will try to show evidence, though indirect, that favors explicit quantification over times in the object language.
We have also considered but dismissed a theory that explains the speech time dependency by incorporating the speech time into the semantics of operators as a version of absolute theories of tense. This analysis predicts no scope relation between two tense operators when one is embedded under the other. This seems correct when the future will is embedded under a past tense operator, but not when a past tense operator is embedded under the future. As Ogihara (1996) argues, the past tense operator does not seem to be inherently speech time sensitive. The fact that the past tense operator sometimes exhibits a speech time dependency, but not always, suggests that the effect should not be accounted for as a lexical property.
1.4. Context Dependency of Tense Interpretation: Is Tense an Existential Quantifier?
In the previous section, we assumed that tense introduces an existential quantifier over times, following Prior (1967), and considered different ways of accounting for the data that have
been presented as a problem of Priorian theory. This first assumption has also been challenged, and this is the topic of this section. Among the proponents of tense without existential quantification, there are at least two subgroups, depending on whether or not explicit quantification over times in the object language is employed. One is the referential theory of tenses advocated by Partee (1973), where she treats tenses as pronominal
elements. This analysis necessarily implies explicit quantification over times in the object language, assuming that pronominal elements such as pronouns and reflexives are variables in the object language.26 Theories of tense without existential quantification do not
necessarily imply explicit quantification over times in the object language, however. A system proposed in Dowty (1982) is a two-dimensional tense system, where tenses manipulate times only in the meta-language.
We will start our discussion with the famous stove example:
(34) I didn't turn off the stove
Partee argues that this example poses a problem to the Priorian view of tenses like the following.
(35) Where is a tenseless sentence,
[[Past ]]t = 1 iff there is a time t' such that t' < t and [[]]t' = 1
We can derive two distinct LFs for the sentence depending on whether the past tense or the negation takes wide scope. We predict that the sentence has two distinct truth conditions.
26 Treating pronominal elements such as pronouns and reflexives as expressions denoting individuals (i.e., of type <e>) is a common practice in the syntactic literature. But this does not mean that this is the only way to analyze pronominal elements. Prior and Fine (1977) have shown that pronouns can be analyzed as operators. If so, analyzing tenses as pronominal elements does not imply explicit quantification over times. I thank Barbara Partee (p.c.) for pointing this out to me.
(36) a. [[Past [not [ I turn off the stove]] ]]t = 1 iff t'[t' < t & ¬turn-off-the-stove(I)(t)]
b. [[not [Past [ I turn off the stove]] ]]t = 1 iff ¬t'[t' < t & turn-off-the-stove(I)(t)]
(36a) asserts the existence of the time at which I didn't turn off the stove while (36b) means that I have never turned off the stove. (36a) would almost always be true if uttered by an ordinary adult individual and (36b) would almost always be false. Suppose that I was to go out and it took me twenty minutes to get ready, getting dressed, closing the windows and so on. When I utter the sentence later on, the contextually salient interval is the time while I was getting ready. When uttered halfway down the turnpike, the sentence means neither (36a) nor (36b). Rather, it means that during the twenty-minute interval before I left the house, I didn't turn off the stove.
Partee (1973) claims that this kind of context dependent use of tenses is analogous to the deictic usage of pronouns like the following:
(37) She left me
Further analogies between pronouns and tenses are also observed27:
(38) Definite antecedents
a. Sheila had a party last Friday and Sam got drunk b. When John saw Mary, she crossed the street
c. Sam is married. He has three children.
27 All the examples are from Partee (1973) or Partee (1984) except for the example (41a, b). The donkey sentence (41b) is originally due to Geach (1962).
(39) Indefinite antecedents
a. Mary woke up sometime during the night. She turned the light on
b. Peter owns a donkey. He takes good care of it.
(40) Bound variable28
a. Whenever Mary telephoned Sam was asleep
b. Whenever Mary wrote a letter, Sam answered it two days later
c. No woman fully appreciates her mother
(41) 'Donkey sentences'
a. Every friend of mine who visited Boston said that she had a good time there
b. Every farmer who owns a donkey takes good care of it
Partee claims that just like pronouns, tenses can be referential, anaphoric, or bound. What do these analogies tell us? Partee (1973) claims that these analogies suggest that tenses and pronouns should be treated on a par. To make this a substantial claim, we have to know what pronouns are. Pronouns are treated as variables of an individual type, i.e., of type <e>, and their interpretation is variable assignment dependent. Thus we have the following:
(42) a. [[hei]]g,c = g(i) b. [[shei]]g,c = g(i)
28 Note that in (40b) it is not the past tense on the verb answer that is bound by the universal quantifier introduced by whenever, but an implicit variable associated with later as represented below.
(i) t[Mary writes a letter at t and t is before the speech time t'[t' is two days after the day of t and Sam answers it at t']
These denotations obviously miss the gender difference between the two pronoun he and she. He, for instance, can only be referential, anaphoric, or bound by an NP whose gender
is identified as a male individual.29 This gender distinction may be incorporated into the definedness condition.
(43) a. [[hei]]g,c is only defined if g(i) is a male individual When defined, [[hei]]g,c = g(i)
b. [[shei]]g,c is only defined if g(i) is a female individual When defined, [[shei]]g,c = g(i)
This explains why the anaphoric or bound variable reading is not available for the pronouns in the following sentences.
(44) a. John said that she was sick
b. No woman fully appreciates his mother
The definedness condition is not enough for the construal of pronouns that are not
syntactically bound. Consider the second sentence in the example (38c), and suppose that the pronoun he has an index i. Then consider the truth conditions of the sentence under a variable assignment that assigns the index i the male individual Mark. The sentence should mean that Mark has three children, and it is true when Mark in fact has three children and false when he doesn't. But if the speaker of the sentences in (38c) tries to convey this information, i.e., Sam is married and Mark has three children, the usage of the pronoun he
29 There are exceptions to this generalization. One is a case like the following, when NPs that bind a pronoun are 'neutral' in the sense that they include both men and women.
(i) Everybody likes his mother
I do not know how 'exceptions' like this should be treated in the grammar.
in the second sentence does not seem appropriate. The use of a free pronoun should be more constrained; its value should be given by the speech context. Let us formulate this restriction in the following way:30
(45) Appropriateness Condition
A context c is appropriate for an LF only if c determines a variable assignment gc whose domain includes every index which has a free occurrence in .
When the second sentence in (38c) is uttered following the first one, and no other
extralinguistic factor (such as pointing to a man who just walked into the room) is involved, the only way to appropriately use the free pronoun he in this context is to mean he denotes Sam.
If we assume the semantics of pronouns as above, and try to analyze tenses on a par with pronouns, we are led to the hypothesis that tenses are also variables. Partee argues along this line and suggests that tenses are time denoting variables that can be anaphoric, referential, or bound. One way to translate her suggestion into our framework is as
follows31: the past tense morpheme is a time variable and it saturates the time argument slot.
Like pronouns, the value of the variable is assignment function dependent. Under this analysis, the semantic contribution of the past tense morpheme is that it restricts its value to a time prior to the speech time. We incorporate it in the definedness condition on the past tense as in (46). We assume here that sentences are evaluated with respect to a speech context c and each speech context determines the speech time tc.
30 From Heim and Kratzer (1998).
31 This particular implementation is from Kratzer (1995) and Heim (1994).
(46) [[pasti]]g,c is only defined if g(i) < tc.
When defined, [[pasti]]g,c = g(i)
The Partee sentence will have the LF in (47b). With the semantics of the past tense and the predicate turn-off-the-stove and when defined, it is true iff I didn't turn off the stove at g(i).
(47) a. I didn't turn off the stove
b. not [TP pasti [VP I turn off the stove]]
c. ¬ turn-off-the-stove(I)(pasti)
The analysis implies that the event times of predicates are explicitly represented in the LF syntax as tense morphemes, denoting times. And it presupposes that there is a way to introduce those variables somehow. Here, we assume that predicates have an extra argument slot for times. Therefore, the analysis is subject to the same criticism Kamp (1973) and Cresswell (1990) present to theories with explicit quantification over time, that this complicates our analysis of syntactic structures.
But apart from conceptual issues, does this really capture the intuition? Ogihara (1989, 1995b, 1996) argues that it does not. In the scenario above, the contextually salient interval is the twenty-minute interval while I was getting ready. But it is wrong to say that that interval is the interval at which I didn't turn off the stove, since turning off the stove does not take more than a few seconds. In order for the sentence to be felicitous, the speaker has to have such a short interval in mind. This is because the time variable pasti (47b) is free, and therefore it is subject to the appropriateness condition.
Rather, the meaning we want to attribute to the sentence in this context is that there is no time within the twenty-minute interval before I got out of the house at which I turned off the stove. That is, the truth conditions we want are something like (48), with an existential quantifier.
(48) ¬t[t tR and turn-off-the-stove(I)(t)], where tR is the contextually salient interval, i.e., the twenty-minute interval before I got out of the house.
So where does this existential quantifier come from? If we try to follow the original Partee theory of 1973, one solution is to build an existential quantifier into the semantics of verbs, that is, switch from truth at an interval to truth in an interval.32
(49) [[turn-off-the-stove]] = f: De D<i,t>
For all x De and t Di, f(x)(t) = 1 iff x turns off the stove in t
(I.e., f(x)(t) = 1 iff there is a time t' t such that x turns off the stove at t')
In this theory, tenses are referential and denote contextually salient intervals. In the above scenario, it is the twenty-minute interval before I left the house. With an existential quantifier built into the semantics of the verb, we correctly predict the truth conditions in (48).
Note that the event times of predicates are no longer represented in the object language in this system. Only the reference times are. This creates another problem.
Recall the point made by Vlach (1973). He established that the natural language tense system should be able to keep track of all intermediate evaluation times as well as the original evaluation time. Intermediate evaluation times in Vlach's system partially
correspond to the event times of predicates in the system we are currently considering. If we build an existential quantifier into the semantics of predicates as above, event times are not overtly realized in the LF syntax. This is problematic. Consider the following example in a context in which students are told to talk to a doctor for annual check-up during a particular period, say between May 23rd to 27th.
32 See Cresswell (1985) for more discussion of truth at or in an interval.
(50) Every student talked to a doctor who was available then
We understand the reference time, i.e., the time the matrix past tense denotes, to be that five- day period. And the adverb then can be understood to refer to that period. But there is another interpretation in which then gets a bound variable interpretation; every student talked to a doctor who was available during the time he/she talked but not during the entire five day period. In this system, however, the time of each student's talking is not syntactically
represented as a time variable, and therefore cannot act as the antecedent of then.
Alternatively, we may give up analyzing tenses themselves as referential. In her 1984 paper, Partee in fact argues against her own earlier claim that tenses are referential.
There she claims, following Bäuerle (1977, 1979) and Hinrichs (1981), that what is referential is the reference time in the sense of Reichenbach (1947). Here is an
implementation of the idea. The past tense is a function from intervals to functions from properties of times to propositions, and it involves existential quantification over times. The first argument of the past tense is its reference time (tR) and the semantics of the past tense requires it to be a past interval.
(51) a. [[past]]g,c = f: Di D<it,t>
For all t Di and p D<i,t>, f(t)(p) = 1 iff t' such that t' t and p(t') = 1.
b. [[past [ tR] ]]g,c is only defined if g(tR) < tc.
When defined, [[past [ tR] ]]g,c = f: D<i,t> Dt
For all p D<i,t>, f(p) = 1 iff t' such that t' tR and p(t') = 1.
The stove example has the LF in (52b) under this analysis.33
33 In order to derive the right interpretation, it has to be stipulated that negation takes a sentential scope. This stipulation is not compatible with the standardly assumed structure of inflectional categories. We will leave this problem open.
(52) a. I didn't turn off the stove
b. not [TP past [tR] [VP I turn off the stove]]
c. ¬t[t tR and turn-off-the-stove(I)(t)]
The new analysis captures the right intuition.
Both of Partee's theories discussed above may be classified as absolute theories of tense. Their definedness condition refers to the speech time, and this is where the
"pastness" of sentences with the past tense originated. Therefore, these theories face the same problem as the sentential operator treatment of tenses that incorporates the speech time dependency into the semantics of the operators. We considered the following examples:
(53) a. I will marry a man who went to Harvard
b. I thought that the student would not admit that he cheated c. David will say that he was out of town
d. No matter what you give him to eat, he will eat it and tell you that he liked it
We want the embedded past tenses to be evaluated with respect to the future event times of the next higher clauses. Clearly, these examples show that some element that can shift the evaluation time, something analogous to a Priorian operator, is necessary.34
Partee (1984) also discusses examples that suggest Priorian tense semantics.35
(54) a. Who killed Julius Caesar?
34 This does not necessarily deny that the past tense in sentences like the stove example cannot be analyzed as an absolute tense as we did following Partee. It could be that the past tense is ambiguous between an absolute interpretation (as in the stove example) and a shifting interpretation (as in the examples in (53)). This is in fact the line Kratzer (1998b) takes. We do not have an argument against positing this ambiguity, but we will see that both interpretations may be derived by a single denotation of the past tense morpheme.
35(a) is from Partee (1984) and (b) is a variant of an example from Partee (1973).
